On a new application of the path integrals in polymer statistical physics

TL;DR

This paper introduces a novel path integral approach to compute probability distributions of quadratic properties of Gaussian polymers, providing exact relations and asymptotic evaluations for large and small variable limits.

Contribution

It presents a new application of path integrals in polymer physics, deriving exact characteristic functions and cumulants for key quadratic quantities.

Findings

Exact relations for characteristic functions and cumulants obtained.

Asymptotic probability distributions evaluated for extreme variable values.

Method offers a new analytical tool for polymer statistical analysis.

Abstract

We propose a new approach based on the path integral formalism to the calculation of the probability distribution functions of quadratic quantities of the Gaussian polymer chain in d-dimensional space, such as the radius of gyration and potential energy in the parabolic well. In both cases we obtain the exact relations for the characteristic function and cumulants. Using the standard steepest-descent method, we evaluate the probability distribution functions in two limiting cases of the large and small values of corresponding variables.